What is the integral of 1/(cos^2(x+1)) ?

The integral of 1/(cos^2(x+1)) is tan(x+1)+C

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integral of 1/(cos^2(x+1))

\int \frac{1}{cos ^{2} ( x + 1 )} d x

tan (x + 1) + C

Solution steps

\int \frac{1}{cos ^{2} ( x + 1 )} d x

Apply u-substitution

: \int sec^{2} (u) d u

= \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= tan (u)

Substitute back

u = x + 1

= tan (x + 1)

Add a constant to the solution

= tan (x + 1) + C

\int x ln (1 + x) d x

\int_{0}^{4} (4 x) - (2 x) d x

2 x^{2} + 5 x

x \to 0 lim (x^{3} sin (\frac{1}{x}))

f (x) = 2 sec (x)

What is the integral of 1/(cos^2(x+1)) ?
The integral of 1/(cos^2(x+1)) is tan(x+1)+C